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An analysis of single-index model with monotonic link function. (English) Zbl 1150.62026

Summary: The single-index model with monotonic link function is investigated. Firstly, it is shown that the link function \(h (\cdot)\) can be viewed by a graphic method. That is, the plot with the fitted response \(\Hat y\) on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess \(h (\cdot)\). Therefore, the \(I\)-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach.

MSC:

62G99 Nonparametric inference
62A09 Graphical methods in statistics
65C60 Computational problems in statistics (MSC2010)
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